No, I personally would say that schools and applicants do not have the same idea of "fit." Applicants are picking based on more than academic interests, including where they want to live, the type of people they want to socialize with, the type of environment they want to work in, the type of career they want to have afterwards, how much the program can pay them... For the committees, it's purely academic, but also random as hell. Decisions aren't made on who is the "smartest" or "best," but rather who's on the committee that year, who took too many students last year, who hasn't taken students in awhile... The applicants aren't aware of these arbitrary factors, so all applicants can do is present the most accurate depiction of who they are as a student and hope that there's a need in the program for a student like them.

Just putting it out there that I’m available to answer questions anyone might have, having gone through the process just a few months ago. Feel free to PM me. My notifications for PM’s are on. Good luck to everyone—it’s an exciting time!

I literally scored in the twentieth percentile for quant. It’s probably the least important part of your application. I wouldn’t even consider it part of your application, but you do have to submit it as part of your test scores.

First of all: you should absolutely be excited! This is amazing.
There are other things to consider though.
If the costs are low, I say go for it. I do mean really low. I wouldn’t spend more than $150 on it. This will not only look good on your CV, but this is also something you can talk about in your SOP. I mentioned that I attended a conference when I was an undergrad (didn’t even read my work at one, literally just sat in the audience lol) and I was told it demonstrated dedication, maturity, and a sense of preparedness. But it wasn’t some huge defining part of my application—just a, “oh, she went to that conference, cool...”
I would make sure it’s a reputable grad conference. If it’s one no one has ever heard of, and if you’re going to spend some money on it, then I’d be wary because I will say it’s not likely that it’ll impact your application that much. That money could be better spent towards application fees, or maybe even some extra GRE materials... From my talks with other students, it’s not unheard of, or even necessarily extremely uncommon, for high-performing undergrads to have presented at a conference. That doesn’t make it any less of an achievement, though.
Another thought (which I think is the way to go here): you can mention you were invited to speak at this conference without having to actually pay to go to the conference. Any professor in any department would understand you not wanting to pay those fees. But it’s easy to weave it into your SOP and would be equally as impressive. “My senior year of college, I was invited to conference x to speak on project y. While I was not able to attend the conference, the research I did in that paper helped me further my questions on blah, blah, blah...”

I'm probably going to sign off on GradCafe for the foreseeable future! This place was incredibly helpful to me throughout this process, but I think I'm going to dedicate the rest of spring/summer to just reading, relaxing, and trying to prepare myself for the next 6+ years. (Also I should start learning French.)
I do plan to check back in periodically (plus I'm sure I'll have questions or see a discussion I'd like to chime in on), but if any future applicants look back through this thread and have questions about applications/programs/etc, feel free to PM me! Hopefully I will check in frequently enough to see it and respond. I'm not sure how helpful my advice may be, but I thought I'd put that offer out there. Over the past few months, I've become really upset with the admission process and the way it makes applicants question their worth as scholars... I know my ass was saved a few times by people who were kind enough to sit down and give me pointers, so I'm happy to do that as much as I can for anyone else.
I'm really proud of the group we had here this year. I'm not sure if this is common or not, but I was pleasantly surprised by the support we gave each other, and the genuine happiness we felt for others success even in the midst of our own "failures" (yuck, that's definitely not the right word). I'm really hoping this is representative of graduate students on a larger scale, but I guess I'll have to wait until the fall to find out more about that. Thanks for everything guys!! Hope to see you around.

To anyone on NYU's waitlist: I've heard that a greater number of students accepted their initial offer than expected, so they likely won't be using the waitlist. Just wanted to give you guys a heads up about that, given the approaching deadline and the need to make final decisions.

For me, having that full year off was crucial. I didn't feel rushed in getting my materials together, and was able to dedicate much of the fall/early winter to nothing but my application. I don't think I would've had as strong of an application if I had attempted to rush it, or if my attention was hindered by school work. Also, it was an incredibly peaceful year of self reflection. Having time away from school allowed me to reflect on what it truly was that I wanted to study, and reaffirmed to me that going back to school was the right decision.

I currently live in NYC! Whenever someone talks to me about the cost of NYC, I always like to point out that it's the most populous city in America for a reason! Millions of people live here every day, and not all of them are making above 50k. It's VERY possible to live here.
The difference between NYC and other cities is that your primary expense will be rent and you will almost assuredly not have the luxury of living alone. However, it isn't this completely unlivable place. It simply requires you to adjust your way of life if you want to reside here: living with roommates, having a long commute...AKA a 3 bedroom apartment in Brooklyn with two other people, essentially. It's doable. It just might not be everyone's idea of fun or how you want to spend the next 6 years.
NYU's stipend is very livable in my opinion. Columbia's stipend is significantly less than NYU's, and I'd also consider it livable.